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Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions

Institute of Scientific Research and Development, Tomsk State Pedagogical University (TSPU), 60 Kievskaya St., Tomsk 634041, Russia

Laboratory for Theoretical Cosmology, International Center of Gravity and Cosmos, Tomsk State University of Control Systems and Radio Electronics (TUSUR), 36, Lenin Avenue, Tomsk 634050, Russia

E-mail Address: obukhov@tspu.edu.ru

Corresponding author.

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S. V. Chervon

https://orcid.org/0000-0001-8898-3694

Laboratory of Gravitation, Cosmology, Astrophysics, Ulyanovsk State Pedagogical University, Lenin’s square, 4/5, Ulyanovsk 432071, Russia

Physics Department, Bauman Moscow State Technical University, 2nd Baumanskaya Street 5, Moscow 105005, Russia

E-mail Address: chervon.sergey@gmail.com

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, and

D. V. Kartashov

https://orcid.org/0009-0008-9863-0874

Institute of Scientific Research and Development, Tomsk State Pedagogical University (TSPU), 60 Kievskaya St., Tomsk 634041, Russia

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https://doi.org/10.1142/S0219887824500920Cited by:2 (Source: Crossref)

Abstract

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions $G_{4} (N)$ . The potentials of the admissible electromagnetic fields admit the existence of the algebra of motion integrals of the Hamilton–Jacobi and Klein–Gordon–Fock equations which is isomorphic to the algebra of the group operators for the same group $G_{4} (N)$ .

Keywords:

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